On the stability of a forward-backward heat equation

Details On the stability of a forward-backward heat equation On the stability of a forward-backward heat equation

2011-10-31

arxiv.org/abs/1110.6869v1

Mathematics

Spectral Theory

21 pages, 3 figures

Scientific paper

In this paper we examine spectral properties of a family of periodic singular Sturm-Liouville problems which are highly non-self-adjoint but have purely real spectrum. The problem originated from the study of the lubrication approximation of a viscous fluid film in the inner surface of a rotating cylinder and has received a substantial amount of attention in recent years. Our main focus will be the determination of Schatten class inclusions for the resolvent operator and regularity properties of the associated evolution equation.

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